Question

1. which set of numbers forms a right triangle? a. 4, 5, 9 b. 9, 16, 25 c. 8, 9, 10 d. 6, 8, 10

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (the longest side).

Step2: Check option C

Let \(a = 8\), \(b=9\), \(c = 10\).
Calculate \(a^{2}+b^{2}=8^{2}+9^{2}=64 + 81=145\).
Calculate \(c^{2}=10^{2}=100\). Since \(145
eq100\), option C is wrong.

Step3: Check option B

Let \(a = 9\), \(b = 16\), \(c=25\).
Calculate \(a^{2}+b^{2}=9^{2}+16^{2}=81+256 = 337\).
Calculate \(c^{2}=25^{2}=625\). Since \(337
eq625\), option B is wrong.

Step4: Check option A

Let \(a = 4\), \(b = 5\), \(c = 9\).
Calculate \(a^{2}+b^{2}=4^{2}+5^{2}=16 + 25=41\).
Calculate \(c^{2}=9^{2}=81\). Since \(41
eq81\), option A is wrong.

Step5: Check option D

Let \(a = 6\), \(b = 8\), \(c = 10\).
Calculate \(a^{2}+b^{2}=6^{2}+8^{2}=36+64 = 100\).
Calculate \(c^{2}=10^{2}=100\). Since \(a^{2}+b^{2}=c^{2}\), option D satisfies the Pythagorean theorem.

Answer:

D. 6, 8, 10